Graphene's Dirac Fermions and A2 Root System Symmetry in Hexagonal Lattices — E8 Intelligence Research

Andrew Stewart Caldin

doi:10.5281/zenodo.21897981

August 12, 2026Open Access

Graphene's Dirac Fermions and A2 Root System Symmetry in Hexagonal Lattices — E8 Intelligence Research

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Key Points

To establish the mathematical and geometric connection between massless Dirac fermions in 2D hexagonal graphene lattices and crystallographic A2 root systems.
Formulated 2D Dirac equations alongside real-space and reciprocal lattice vectors for the hexagonal lattice.
Calculated Berry curvature distribution concentrated at the K and K' symmetry points of the Brillouin zone.
Evaluated the crystallographic 60° and 120° angle structures and geometric ratios relative to the SU(3) A2 root system.
Demonstrated that the 2D hexagonal lattice serves as a direct physical realization of the A2 root system of SU(3) with characteristic 60° and 120° symmetries.
Identified that the √3 (≈1.732) ratio governs lattice spacing and Dirac cone geometry, alongside concentrated Berry curvature at K and K' points.
Confirmed that the electronic structure geometry exhibits no direct dependence on the golden ratio (0.618, 1.618) or base-60 numerical systems.

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Implication

Theoretical analysis demonstrates that graphene hexagonal lattices realize the A2 root system and SU(3) symmetry, highlighting geometric links between condensed matter topology and Lie algebras.

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Cite This Study

Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a7ee587b70b84ec8b914668 https://doi.org/10.5281/zenodo.21897981

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Graphene's Dirac Fermions and A2 Root System Symmetry in Hexagonal Lattices — E8 Intelligence Research

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Discussion

Cite This Study

Graphene's Dirac Fermions and A2 Root System Symmetry in Hexagonal Lattices — E8 Intelligence Research

Key Points

No abstract yet

Implication

Discussion

Cite This Study

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